- #1
sudipmaity
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Homework Statement
The ground state wavefuntion
of a system in spherical polar
coordinates is given by:
Ψ (r,θ, φ)= (A/r) [exp (-ar) -
exp (-br)] where a, b, A are
constants.
i) Determine A as a function
of a and b, so as to normalize
the wavefuntion.
ii) From Schrödinger equation
find V (r) in terms of a and b
iii) From potential behaviour
find the energy eigenvalue if
b=6a in the ground state.
Homework Equations
integral |ψ|^2 dτ=1
Hψ=Eψ
H= -hbar/2m grad^2 + V
The Attempt at a Solution
I integrated | ψ|^2 r^2 dr
sinθ dθ dφ =1
I found A= {1/a-b}[ab* (a
+b) /2π]^(1/2)
After putting the wavefuntion
in time independent
schrodinger's (Hψ=Eψ)the
calculation is getting pretty
elaborate.Cant figure out how
to find the potential.This is a
University exam question and
each of the three question
carried 2 marks.please help
me calculate the potential.